Math @ Duke

Publications [#323246] of JianGuo Liu
Papers Published
 Liu, JG; Xu, X, Existence theorems for a multidimensional crystal surface model,
Siam Journal on Mathematical Analysis, vol. 48 no. 6
(January, 2016),
pp. 36673687, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/06/17)
Abstract: © 2016 Society for Industrial and Applied Mathematics. In this paper we study the existence assertion of the initial boundary value problem for the equation @u/@t = ΔeΔu. This problem arises in the mathematical description of the evolution of crystal surfaces. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow "cancels" it out. The net result is that we obtain a solution u that satisfies the equation and the initial boundary conditions in the almost everywhere (a.e.) sense.


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